Basic statistics has its Chebyshev inequality, martingale theory has its maximal inequalities, Markov processes have large deviations, but all pale in comparison to the power and simplicity of the coresponding basic inequality of Gaussian processes. This inequality was discovered independently, and established with very different proofs, by Borell [30] and Tsirelson, Ibragimov, and Sudakov (TIS) [160]. For brevity, we shall call it the Borell–TIS inequality. In the following section we shall treat it in some detail.


Gaussian Process Isoperimetric Inequality Gaussian Variable Chebyshev Inequality Exponential Moment 
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© Springer Science+Business Media LLC 2007

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